Номер 9, страница 161 - гдз по английскому языку 10 класс (enjoy english) учебник Биболетова, Бабушис

9 Do you remember how to solve a system of linear equations? Study the example below to make sure about one of the ways.

X + Y = 4

Y + XY = 6

1 First, we express Y through X in the first equation. Then we take Y out of the brackets in the second equation.

Y = 4 - X

Y × (1 + X) = 6

2 We write the Y-equivalent from the first equation in the second equation. So, we have the following:

(4 - X) × (1 + X) = 6

3 We multiply (4 - X) by (1 + X) and write the new expression in the left-hand side of the equation. The right-hand side is still the same.

4 + 4X - X - X = 6

4 After that, we transfer everything to the left-hand side to make the expression equal to zero.

-X² + 3X - 2 = 0

5 Then we change the signs to make the quadratic equation look more conventional.

X² - 3X + 2 = 0

6 To solve the quadratic equation we apply the quadratic formula

X = (-b ± √(b² - 4ac)) / 2a

which is true for any quadratic equation

aX² + bX + c = 0

We see that in our equation

b is equal to –3,

a is equal to 1

and c is equal to 2.

So, we use these numbers instead of the

letters and get the following:

X = (3 ± √(3² - 4×2)) / 2

7 Then we simplify the right-hand side.

X = (3 ± √1) / 2

8 The sign ± demonstrates that X can take two different values. We need to solve the expression for X₁ and X₂.

X₁ = (3 + 1) / 2

X₂ = (3 - 1) / 2

X₁ = 2 (X₁ is equal to two)

X₂ = 1 (X₂ is equal to one)

9 Now we know the value of X₁ and X₂, and we need to find out Y₁ and Y₂. Let's express them through X₁ and X₂ (see step 2).

Y₁ = 4 - 2 = 2

(Y₁ is equal to four minus two and is equal to two)

Y₂ = 4 - 1 = 3

(Y₂ is equal to four minus one and is equal to three)

10 Now we can see that the system of equations has two solutions. We write down both of them as necessary.

Solution: (2; 2) (1; 3)

9 Помнишь ли ты, как решать систему линейных уравнений? Изучи пример ниже, чтобы убедиться в одном из способов.

Ответ:

Yes, I remember how to solve systems of linear equations. I have studied the example and now I am sure about one of the ways.

Да, я помню, как решать системы линейных уравнений. Я изучил пример и теперь уверен в одном из способов.